Three boxes, A, B and C, contained 328 marbles. Ian added some marbles into Box A and the number of marbles in Box A tripled. He took out half of the number of marbles from Box B and removed 55 marbles from Box C. As a result, the ratio of the number of marbles in Box A, Box B and Box C became 6 : 4 : 11. What was the ratio of the number of marbles in Box C to the total number of marbles in Box A and Box B at first? Give the answer in its lowest term.
| |
Box A |
Box B |
Box C |
Total |
| Before |
1x2 =
2 u |
2x4 =
8 u |
11 u + 55 |
328 |
| Change |
+ 2x2 =
+ 4 u |
- 1x4 =
- 4 u |
- 55 |
|
| After |
3x2 =
6 u |
1x4 =
4 u |
|
|
Comparing the
3 boxes |
6 u
|
4 u |
11 u |
|
The number of marbles in Box A in the end is the same. Make the number of marbles in Box A in the end the same. LCM of 3 and 6 is 6.
The number of marbles in Box B in the end is the same. Make the number of marbles in Box B in the end the same. LCM of 1 and 4 is 4.
Total number of marbles at first
= 2 u + 8 u + 11 u + 55
= 21 u + 55
21 u + 55 = 328
21 u = 328 - 55
21 u = 273
1 u = 273 ÷ 21 = 13
Number of marbles in Box C at first
= 11 u + 55
= 11 x 13 + 55
= 143 + 55
= 198
Number of marbles in Box A and Box B at first
= 328 - 198
= 130
Box C : Box A and Box B
198 : 130
(÷2)99 : 65
Answer(s): 99 : 65
